Spherical Models

I started constructing these spherical (and ellipsoidal) models after
constructing several polyhedral models, with the faces randomly chosen
from the planes tangent to a sphere.

These were initially just an attempt to construct something funky looking
using the same construction methods as I'd used for a number of models
of regular solids. However, as I increased the complexity, I ran into
problems in which small inaccuracies accumulated at some types of vertices.
Currently an 81-faced model lies unfinished on my desk, as I think about
how to compensate for paper thickness.

The edge models all have a similar construction method, which is adapted
from that described in Spherical Models
by Magnus J. Wenninger.

Models are listed in chronological order, with construction details and
larger photos linked from the thumbnails.

This pair is generated from 45 points chosen from a uniformly at random
on the surface of a sphere. On the left are the Voronoi cells, while on
the right, the Delaunay triangulation.

This considerably smaller pair is generated from 33 points that were
iteratively moved away from each other. Just over two inches in diameter
they were intended as holiday tree decorations.

Here the 41 points are chosen along a spiral, and the Delaunay
triangulation is what is modeled. I made no effort to randomise or
adjust the spacing; it's simply linear along the parameter of the spiral.

Instead of lying on a sphere, the edges now lie on an ellipsoid.
Here's the first pair of such models.

This is my second attempt at a spiral. Although people seem to need to
turn it around in their hands a few times to find it the spiral, I'm
very happy with the two color effect, when you look at it from the side.

Here's a larger ellipsoid, which is made using a slightly modified
construction method.

Picture three cylinders (all the same) intersecting at right angles.
Here's what the intersection looks like.